On the past two quizzes, a student scored a 75 and 83. Write and solve a compound inequality to find the possible values for the 3rd quiz score that would give her an average between 85 and 90, inclusive.

average = sum of all values/number of values
i have no clue how to do this im screaminh pleas teach me

Not quite.

85*3 <= 75+83+x <= 90*3

Don't worry, I'm here to help! Let's break this down step by step.

To find the possible values for the 3rd quiz score, we need to determine the range that will give the student an average between 85 and 90, inclusive.

First, let's find the lowest average possible. To do this, we'll add up the scores from the first two quizzes and divide it by 2 (since we have 2 quizzes so far). This gives us:

(75 + 83) / 2 = 158 / 2 = 79

Now, let's find the highest possible average. Since we want an average between 85 and 90 inclusive, the highest average will be 90.

Since there will be a total of 3 quizzes, we can now set up a compound inequality to find the range of scores for the 3rd quiz:

79 ≤ (75 + 83 + x) / 3 ≤ 90

Let's simplify this further:

79 ≤ (158 + x) / 3 ≤ 90 (multiply by 3)

237 ≤ 158 + x ≤ 270 (subtract 158 from all parts)

237 - 158 ≤ x ≤ 270 - 158

79 ≤ x ≤ 112

Therefore, the possible values for the 3rd quiz score, in order to have an average between 85 and 90 inclusive, are any scores between 79 and 112.

I hope this helps! Let me know if you have any more questions.

No need to panic! I'm here to help you understand how to tackle this problem step by step.

To find the possible values for the 3rd quiz score that would give the student an average between 85 and 90 (inclusive) after the three quizzes, we can set up a compound inequality. Here's how you can do it:

Step 1: Calculate the desired average between 85 and 90 (inclusive):
- The average is found by dividing the sum of the three quiz scores by 3.
- For this case, the average should be ≥ 85 and ≤ 90.

Step 2: Express the compound inequality in terms of the 3rd quiz score:
- Let's assume the 3rd quiz score as 'x'.
- Then, we can set up the compound inequality as follows:
85 ≤ (75 + 83 + x)/3 ≤ 90

Step 3: Simplify the compound inequality:
- Multiply both sides of the equation by 3 to eliminate the division:
255 ≤ 75 + 83 + x ≤ 270

Step 4: Combine like terms:
- Simplify the inequality:
255 ≤ 158 + x ≤ 270

Step 5: Isolate the variable:
- Subtract 158 from all parts of the compound inequality:
255 - 158 ≤ x ≤ 270 - 158

Step 6: Solve for x:
- Calculate the values of x:
97 ≤ x ≤ 112

Therefore, for the student to obtain an average between 85 and 90 (inclusive) after the three quizzes, the 3rd quiz score should be between 97 and 112, inclusive.

85<= 75+83+x <= 90

Don't worry, I'll guide you step-by-step through solving this problem!

To find the possible values for the third quiz score, we need to determine the range of values that would give the student an average between 85 and 90, inclusive.

Let's start by setting up the equation for the average:
Average = (75 + 83 + x)/3

To make sure the average falls between 85 and 90, inclusive, we can write the compound inequality:
85 ≤ Average ≤ 90

Now, let's substitute the expression for the average into the compound inequality:
85 ≤ (75 + 83 + x)/3 ≤ 90

To solve this compound inequality, we'll solve each side separately. Starting with the left side:

85 ≤ (75 + 83 + x)/3

To eliminate the fraction, we can multiply both sides of the inequality by 3:
3(85) ≤ 75 + 83 + x

Simplifying:
255 ≤ 158 + x

Next, let's solve the right side:

(75 + 83 + x)/3 ≤ 90

Multiply both sides of the inequality by 3:
75 + 83 + x ≤ 3(90)

Simplifying:
158 + x ≤ 270

Now, let's solve each inequality separately:

For the left side:
255 ≤ 158 + x

Subtracting 158 from both sides:
255 - 158 ≤ x
97 ≤ x

For the right side:
158 + x ≤ 270

Subtracting 158 from both sides:
x ≤ 112

Therefore, the possible values for the third quiz score that would give the student an average between 85 and 90, inclusive, are 97 ≤ x ≤ 112.